Gradient-based Meta-Learning requires full backpropagation through the inner optimization procedure, which is a computational nightmare. This paper is able to circumvent this and implicitly compute meta-gradients by the clever introduction of a quadratic regularizer.
OUTLINE:
0:00 - Intro
0:15 - What is Meta-Learning?
9:05 - MAML vs iMAML
16:35 - Problem Formulation
19:15 - Proximal Regularization
26:10 - Derivation of the Implicit Gradient
40:55 - Intuition why this works
43:20 - Full Algorithm
47:40 - Experiments
Paper: arxiv.org/abs/1909.04630
Blog Post: www.inference.vc/notes-on-ima...
Abstract:
A core capability of intelligent systems is the ability to quickly learn new tasks by drawing on prior experience. Gradient (or optimization) based meta-learning has recently emerged as an effective approach for few-shot learning. In this formulation, meta-parameters are learned in the outer loop, while task-specific models are learned in the inner-loop, by using only a small amount of data from the current task. A key challenge in scaling these approaches is the need to differentiate through the inner loop learning process, which can impose considerable computational and memory burdens. By drawing upon implicit differentiation, we develop the implicit MAML algorithm, which depends only on the solution to the inner level optimization and not the path taken by the inner loop optimizer. This effectively decouples the meta-gradient computation from the choice of inner loop optimizer. As a result, our approach is agnostic to the choice of inner loop optimizer and can gracefully handle many gradient steps without vanishing gradients or memory constraints. Theoretically, we prove that implicit MAML can compute accurate meta-gradients with a memory footprint that is, up to small constant factors, no more than that which is required to compute a single inner loop gradient and at no overall increase in the total computational cost. Experimentally, we show that these benefits of implicit MAML translate into empirical gains on few-shot image recognition benchmarks.
Authors: Aravind Rajeswaran, Chelsea Finn, Sham Kakade, Sergey Levine
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